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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation for the last research proposal) Birthplace: Brazil
Daniel Smania holds a PhD (2001) in Mathematics from the National Institute of Pure and Applied Mathematics-IMPA. He is a full professor at the Institute of Mathematical and Computer Sciences-ICMC at the University of São Paulo. He has experience in the area of ​​Mathematics, with an emphasis on Dynamical Systems, working mainly in unidimensional dynamics, especially renormalization theory, and Ergodic Theory, particularly transfer operators and linear response theory. (Source: Lattes Curriculum)
In general terms, the objective of research in the area of Dynamical systems and Ergodic Theory is to describe the long term behavior of systems with an evolution law. There are deep interactions among Dynamical systems, other areas in mathematics like probability theory, geometry and number theory. There are also connections with many sub-areas in physics. In the Smooth ergodic theory, t…
We will study the relation between the spectral properties of the renormalization operator for one-dimensional dynamical systems and the study of the existence, uniqueness and regularity of solutions for the so-called twisted cohomological equation. (AU)
This project introduces the student to the theory of one-dimensional complex dynamical systems using various mathematical tools, specially the theory of conformal Geometry of Riemann surfaces.
This project introduces the student to the ergodic theory of homogeneous flows, and in particular the Ratner's Theorems for unipotent flows. We will also study the connections of this theory with other areas of Mathematics, as Number Theory (Oppenheim's Conjecture) and Geometry (ergodic theory of geodesic flows on constant negative curvature surfaces)
This project introduces the student to the theory of Dynamical Systems through the study of real and complex one-dimensional dynamical systems. We will use both rigorous mathematics and numerical experiments to study such dynamical systems.
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing research grants |
| 4 / 3 | Completed research grants |
| 13 / 11 | Completed scholarships in Brazil |
| 18 / 15 | All research grants and scholarships |
| Associated processes | |
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
| Publications | 11 |
| Citations | 47 |
| Cit./Article | 4.3 |
| Data from Web of Science | |
SMANIA, DANIEL. Shy shadows of infinite-dimensional partially hyperbolic invariant sets. Ergodic Theory and Dynamical Systems, v. 39, n. 5, p. 1361-1400, MAY 2019. Web of Science Citations: 1. (10/08654-1, 08/02841-4, 03/03107-9)
DE LIMA, AMANDA; SMANIA, DANIEL. CENTRAL LIMIT THEOREM FOR THE MODULUS OF CONTINUITY OF AVERAGES OF OBSERVABLES ON TRANSVERSAL FAMILIES OF PIECEWISE EXPANDING UNIMODAL MAPS. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, v. 17, n. 3, p. 673-733, JUN 2018. Web of Science Citations: 1. (10/17419-6)
DE LIMA, AMANDA; SMANIA, DANIEL. Central limit theorem for generalized Weierstrass functions. Stochastics and Dynamics, v. 19, n. 1, FEB 2019. Web of Science Citations: 0. (10/17419-6, 17/06463-3)
DE LIMA, AMANDA; SMANIA, DANIEL. On infinitely cohomologous to zero observables. Ergodic Theory and Dynamical Systems, v. 33, n. 2, p. 375-399, APR 2013. Web of Science Citations: 0. (03/03107-9, 10/17419-6, 10/08654-1, 08/02841-4)
INOQUIO-RENTERIA, IRENE; RIVERA-LETELIER, JUAN. A characterization of hyperbolic potentials of rational maps. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 43, n. 1, p. 99-127, MAR 2012. Web of Science Citations: 15. (10/07267-4)
SMANIA, DANIEL. Solenoidal attractors with bounded combinatorics are shy. ANNALS OF MATHEMATICS, v. 191, n. 1, p. 1-79, JAN 2020. Web of Science Citations: 0. (03/03107-9, 10/08654-1, 17/06463-3, 08/02841-4)
SMANIA, DANIEL; VIDARTE, JOSE. Existence of C-k-Invariant Foliations for Lorenz-Type Maps. Journal of Dynamics and Differential Equations, v. 30, n. 1, p. 227-255, MAR 2018. Web of Science Citations: 0. (09/17153-9)
SIQUEIRA, CARLOS; SMANIA, DANIEL. Holomorphic motions for unicritical correspondences. Nonlinearity, v. 30, n. 8, p. 3104-3125, AUG 2017. Web of Science Citations: 0. (10/17397-2)
CUNHA, KLEYBER; SMANIA, DANIEL. Rigidity for piecewise smooth homeomorphisms on the circle. ADVANCES IN MATHEMATICS, v. 250, p. 193-226, JAN 15 2014. Web of Science Citations: 13. (10/08654-1, 08/02841-4)
BALADI, VIVIANE; SMANIA, DANIEL. LINEAR RESPONSE FOR SMOOTH DEFORMATIONS OF GENERIC NONUNIFORMLY HYPERBOLIC UNIMODAL MAPS. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, v. 45, n. 6, p. 861-926, NOV-DEC 2012. Web of Science Citations: 9. (10/08654-1, 08/02841-4)
CUNHA, KLEYBER; SMANIA, DANIEL. Renormalization for piecewise smooth homeomorphisms on the circle. ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE, v. 30, n. 3, p. 441-462, MAY-JUN 2013. Web of Science Citations: 8. (08/02841-4, 10/08654-1, 07/01045-7)
(References retrieved automatically from State of São Paulo Research Institutions)
LIMA, Amanda de. Famílias transversais de transformações expansoras por pedaços. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (10/17419-6)
LIMA, Carlos Alberto Siqueira. Dinâmica de correspondências holomorfas. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (10/17397-2)
RAMOS, Thiago Rodrigo. Teoria ergódica em fluxos homogêneos e teoremas de Ratner. Dissertação (Mestrado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (16/01411-2)
LIMA, Amanda de. Cohomologia e propriedades estocásticas de transformações expansoras e observáveis lipschitzianos. Dissertação (Mestrado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (04/12117-0)
CUNHA, Kleyber Mota da. Universalidade para homeomorfismos suaves por pedaços do círculo. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (07/01045-7)
VIDARTE, Jose Humberto Bravo. Pertubações suaves de aplicações tipo Lorenz. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (09/17153-9)
VIDARTE, Jose Humberto Bravo. Linearização suave de pontos fixos hiperbólicos. Dissertação (Mestrado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (08/02321-0)
LIMA, Carlos Alberto Siqueira. Dinâmica complexa e formalismo termodinâmico. Dissertação (Mestrado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (08/07356-7)